Embedded Files
TERM 3
AA/AM
FRACTIONS, RATIOS and PROPORTIONS
Fraction of a Number by Addition and Multiplication (Revision)
The student uses repeated halving or known multiplication and division facts to solve problems that involve finding fractions of a set or region, renaming improper fractions, and division with remainders,
e.g., 1/3 of 36, 3 x 10 = 30, 36 – 30 = 6, 6 ÷ 3 = 2, 10 + 2 = 12
e.g., 16/3 = 5 1/3 (using 5 x 3 = 15) 3 1/3
e.g., 8 pies shared among 3 people (8 ÷ 3) by giving each person 2 pies and dividing the remaining 2 pies into thirds (answer: 2 + 1/3 + 1/3 = 2 2/3).
The student uses repeated replication to solve simple problems involving ratios and rates,
e.g. 2:3 ➝ 4:6 ➝ 8:12 etc.
AM (EARLY AP)
ADDITION and SUBTRACTION
Addition and Subtraction of Decimals and Integers
The student can choose appropriately from a broad range of mental strategies to estimate answers and solve addition and subtraction problems involving decimals, integers, and related fractions.The student can also use multiplication and division to solve addition and subtraction problems with whole numbers.
e.g., 3.2 + 1.95 = 3.2 + 2 – 0.05 = 5.2 – 0.05 = 5.15 (compensation);
e.g., 6.03 – 5.8 = □ as 6.03 – 5 – 0.8 = 1.03 – 0.8 = 0.23 (standard place value partitioning) or as 5.8 + □ = 6.03 (reversibility)
e.g., □ + 3.98 = 7.04 as 3.98 + □ = 7.04, □ = 0.02 + 3.04 = 3.06 (commutativity)
e.g., 3/4 + 5/8 = ( 3/4 + 2/8 ) + 3/8 = 1 38 (partitioning fractions)
e.g., 81 – 36 = (9 x 9) – (4 x 9) = 5 x 9 (using factors) e.g., 28 + 33 + 27 + 30 + 32 = 5 􏰀 30 (averaging) e.g., +7 – -3 = +7 + +3 = +10 (equivalent operations on integers)
PROPORTIONS AND FRACTIONS
Fractions, Ratios, and Proportions by Multiplication (Revision)
The student uses a range of multiplication and division strategies to estimate answers and solve problems with fractions, proportions, and ratios. These strategies involve linking division to fractional answers, e.g., 11÷3= 11/3 = 3 2/3
e.g., 13 ÷ 5 = (10 ÷ 5) + (3 ÷ 5) = 2 3/5
The student can also find simple equivalent fractions and rename common fractions as decimals and percentages.
e.g., 5/6 of 24 as 1/6 of 24 = 4, 5 x 4= 20 or 24 – 4 = 20
e.g., 3:5 as □ : 40, 8 x 5 = 40, 8 x 3 = 24
so □ = 24.
e.g., 3/4 = 75/100 = 75%= 0.75
AP
ADDITION AND SUBTRACTION
Addition and Subtraction of Fractions
The student uses a range of mental partitioning strategies to estimate answers and solve problems that involve adding and subtracting fractions, including decimals. The student is able to combine ratios and proportions with different amounts. The strategies include using partitions of fractions and “ones”, and finding equivalent fractions.
e.g.,2 3/4 – 1 2/3 = 1 + (3/4 – 2/3) = 1 + (9/12 – 8/12 ) = 1 1/12
(equivalent fractions) e.g., 20 counters in ratio of 2:3 combined with 60 counters in ratio 8:7 gives a combined ratio of 1:1.
MULTIPLICATION AND DIVISION
Multiplication and Division of Decimals/ Multiplication of Fractions
The student chooses appropriately from a range of mental strategies to estimate answers and solve problems that involve the multiplication of fractions and decimals. The student can also use mental strategies to solve simple division problems with decimals. These strategies involve the partitioning of fractions and relating the parts to one, converting decimals to fractions and vice versa, and recognising the effect of number size on the answer,e.g.,3.6 x 0.75= 3/4 x 3.6 = 2.7 (conversion and commutativity);
e.g., 2/3 x 3/4 = □ as 1/3 x 1/4 = 1/12 so 2/3 of 1/4 = 2/12 so 2/3 x 3/4 = 6/12 = 1/2
e.g., 7.2 ÷ 0.4 as 7.2 ÷ 0.8 = 9 so 7.2 ÷ 0.4 = 18 (doubling and halving with place value).
PROPORTIONS AND RATIOS
Fractions, Ratios, and Proportions by Re-unitising
The student chooses appropriately from a broad range of mental strategies to estimate answers and solve problems involving fractions, proportions, and ratios. These strategies involve using common factors, re-unitising of fractions, decimals and percentages, and finding relationships between and within ratios and simple rates.
e.g., 6:9 as □ :24, 6 x 1 1/2 = 9, □ x 1 1/2 = 24, □ = 16 (between unit multiplying); or 9 x 2 2/3 = 24, 6 x 2 2/3 = 16 (within unit multiplying)
e.g., 65% of 24: 50% of 24 is 12,10% of 24 is 2.4 so 5% is 1.2, 12 + 2.4 + 1.2 = 15.6 (partitioning percentages).
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